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Chapter 4
Graphical Representation
4.1 Broken Line Graphs
4.2 Bar Graphs
4.3 Histograms
4.4 Circle Graphs
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Name: ___________________________________
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4.1 Broken Line Graphs
Introduction
Last chapter we learned about slope and how it can be used to show how something
changes over time and how values relate to each other. In this section, we will learn
about broken line graphs.
A broken line graph uses ______________ connected by line segments to join data.
It is important to put a ________ on your graph, as well as labelling the
__________________ and ________________ axes to display the data shown. When
drawing a graph you decide what different variables go on the axes and the scale the
graph is drawn to. Remember the independent variable goes on the
______________________ axis, and the dependent variable goes on the
_____________________ axis.
Broken line graphs are used to show:
 A trend over time (i.e. average snowfall over twelve months, see below).
 A comparison of sets of data (i.e. the snowfall for different cities).
Example
1) Trevor just opened a small gallery business that sells paintings, prints, jewelry,
carvings and souvenirs. Below is Trevor’s graph of net income for the last year.
In what two months did Trevor
make the most net income? Why
might this be so?
a) From March to August, Trevor’s
net income was relatively low.
Suggest two reasons why this
might be so.
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2) The graph below shows the average snowfall in Regina, Saskatchewan, by
month.
a) What month has the highest average snowfall? How much snow fell that month?
b) During what three months is there no snowfall in Regina?
c) During what month is the average snowfall approximately twice as much as the
average October snowfall?
Worksheet: Introduction to Broken Line Graphs
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Introduction to Broken Line Graphs Worksheet
1) The following graph shows Tom’s spending on lunches for the past week.
a) How much did he spend on lunch on Wednesday? Friday?
b) On what day did he spend the most on lunch, and how much was it? Give one
possible reason why he might have spent so much that day.
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2) Use the graph provided to answer the following questions.
a) What does the graph show?
b) When was Katie’s heart rate the lowest and what was it?
c) When was her heart rate the highest? Why might this have been so?
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3) The graph below shows the value of a particular stock that Vince bought, over a 10week period. If Week 1 is when Vince bought the stock, use the graph to answer the
following questions.
a) At what price did Vince buy the stock?
b) When was the stock worth the most? If Vince had sold it then, what would have
been his profit?
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Graphing Broken Line Graphs
Example 1:
A weather observer for Banff, AB, obtained the following information on average
monthly precipitation there.
a) Graph the data on a broken line graph.
To graph:
1) Label your vertical and horizontal axis with the variable that it represents.
Note: The x-axis generally time.
2) Identify the highest range of the data for each of the variables.
Time (x-axis): range = ___________ months
Profit (y-axis): range = 81.7 = _______ mm ÷ 10 intervals = ______
3) Decide how many units every line on the graph represents for each of your
variables.
4) Be sure to include a title for your graph.
b) Use the graph to predict what the average amount of precipitation might have
been in December. What assumptions have you made?
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Example 2:
Jacob owns a small appliance repair company. He tracked the company’s net profits
over a 10-year period. He is examining the data to see if there is a trend and to decide if
he can increase the salaries of his employees.
a) Graph the data on a broken line graph.
Time (x-axis): range = ___________ years
Profit (y-axis): range = 65 = _______ thousands of dollars ÷ 15 intervals = ______
b) Is there a general trend in the data? If so, what is it? Are there any exceptions to
the trend?
Worksheet: Graphing Broken Line Graphs
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Graphing Broken Line Graphs Worksheet
1) Canadian Review magazine is published once a week. The company keeps track
of the number of magazines sold from different outlets to determine the market
trend. The following data show the number of Canadian Review sales at a local
store over the past eight weeks.
a) Draw a broken line graph to display the data
b) Are sales of the magazine increasing or decreasing?
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2) Stephanie works in a pediatrician’s office. One of her jobs is to track the growth
rate of the babies the doctor treats. The table below shows baby Jessica’s weight
for the first twelve weeks of her life.
a) Draw a broken line graph of the data.
b) Discuss the trend.
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Discussing Trends and Estimating Values
Regular patterns can sometimes be seen in broken line graphs. You may see a regular
decreasing or increasing trend. Two ways of estimating values are used. These are:
Interpolate – when you estimate values ________________________________
_____________________________________________________.
Extrapolate – when you estimate values _______________________________
_____________________________________________________.
Examples:
1) The following graph shows the
growth rate of a bean plant that
David planted in his vegetable
garden.
a) David forgot to record the height
of the bean plant in Week 4.
Use the graph to interpolate the
height of the plant that week.
b) What might the height of the plant be in Week 12?
c) Write a statement describing trends in the bean plant’s growth rate from Week 0
to Week 11.
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2) Brett is a real estate agent and is comparing the average listed price for houses
in Vancouver to those in Regina from 2006 to 2010.
a) Display the information on a broken line graph.
b) What conclusions can you draw from the table about house prices in the two
cities?
c) What can you tell from the graph more readily than from the table?
Worksheet: Interpolation and Extrapolation
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Interpolation and Extrapolation Worksheet
1) Thérèse is on a road trip and is keeping track of
her car’s fuel consumption. The graph below
shows the amount of gas in Thérèse’s car at
different times of the day. Use the graph to
discuss what she may have been doing during
the different time frames.
8 am – 10 am
10 am – 11 am
11 am – 12 pm
12 pm – 5 pm
2) Lumber is often priced in board
feet. A board foot is a piece of
lumber 1 foot long by 1 foot wide by
1 inch thick. The graph below
represents the cost per board foot of
kiln-dried spruce over a period of
one year.
a) What is the general trend in cost
of kiln-dried spruce?
b) The graph does not show the
cost in August. Use the graph to
interpolate the cost of kiln-dried
spruce that month.
d) Based on the general trend in the data, what would you estimate the cost of kilndried spruce to be the following month, March?
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3) Raquel is an agent for a cell phone company. The data below indicates the
number of cell phones sold to males and females in the last year.
a) Use the data to draw a double line graph.
b) Write a statement describing the general trend in cell phone purchases over the
year.
c) Does the graph indicate any relationship between the number of cell phones
purchased by males compared to females? Why or why not?
d) Do you think this graph is a useful representation of the data? If so, why? If not,
what might be a better way to show trends in cell phone purchases?
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Working with Misleading Graphs
The scale and the size of a graph can influence the way you interpret the data. By
changing the scale on an axis or changing the starting point of an axis, you can change
how a viewer interprets the graph; while the graph will still be right, you can influence a
person’s perception of the data.
Examples:
1) The graph below indicates the approximate cost of sheet metal per tonne over a
period of time.
a) What does it appear has happened to the price of sheet metal over time?
b) What are the scale and starting point of the vertical axis?
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c) Redraw the graph starting the vertical axis at zero and using the same
scale. What does this new graph show about the fluctuation in prices?
d) What do you notice about this graph compared to the first graph?
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Graphs can also be misleading when the
intervals of the variables are skewed. A
small interval may make a graph appear to
have a large difference in values.
2) Consider the following example.
a) What does it represent?
b) What is the general trend in Marcia’s
weekly grocery expenditures?
c) What is misleading about the graph?
d) Draw a graph that better represents her expenditures.